The present invention relates to a solid-state laser compensated for pumping-light astigmatism.
In order to efficiently oscillate a solid-state laser, it is important to focus a pumping-light beam on the inside of a gain crystal. This is especially important in the case where a solid-state laser is Kerr-lens mode locked. An ordinary Kerr-lens mode locked laser includes a gain crystal polished to have the Brewster angle and a dichroic concave mirror (which functions as a concave lens for pumping-light) in a cavity. The gain crystal and the dichroic concave mirror cause astigmatism in pumping-light according to an incidence angle. As a result, the focusing of the pumping-light beam is incomplete. At the worst case, the Kerr-lens mode locking is not obtained. In order to overcome the problem, for example, a solid-state laser known as the trademark xe2x80x9cModel 3960xe2x80x9d of Spectra-Physics Lasers Inc. employs a concave mirror to focus pumping light, thereby compensating for the astigmatism caused by the gain crystal and the concave lens.
Adjustment of a pumping light focusing system employing a concave mirror is, however, difficult more than the case of using a lens. Consequently, an easier method using a lens is desired.
On the other hand, widely, a pumping light focusing system is constructed only by lenses without using the concave mirror. In this case, generally, the astigmatism is not taken into account. Recently, however, a technique which suppresses the astigmatism by optimizing overlapping of a cavity mode and the pumping-light beam by empirically tiling a focusing lens by about 5 degrees with respect to the normal has been reported (Y. Chang et al., Applied Physics Letters, Volume 73, Number 15, pp. 2098 to 2100 (1998)).
The tilt of about 5 degrees with respect to the normal described in the paper is, however, an angle adapted only to the reported laser and does not generally optimize the overlapping between the cavity mode and the pumping light beam in an arbitrary solid-state laser. Since the angle is not theoretically determined, there may be an angle which is more suitable.
It is an object of the invention to provide a method which can be generally used for optimally compensating astigmatism in pumping light, a focusing system for pumping light is constructed only by lenses. This method provide a solid-state laser in which astigmatism in pumping light is optimally compensated. Specifically, astigmatism caused by a gain crystal or a concave lens is compensated on purpose by tilting a convex-shaped focusing lens for pumping light about the axis that is perpendicular to the tangential plane, where the tangential plane is defined as that of propagation of light and a sagittal plane is defined as that perpendicular to the tangential plane. When the configuration of the focusing system of pumping light of a laser is determined, the tilting angle of the focusing lens can be theoretically, unconditionally determined.
The focusing lens, the concave lens, and the gain crystal are optical devices which are arranged in series having the same optical axis. A synthetic focusing point of the three elements in a sagittal plane and that in a tangential plane are independently calculated as functions of the tilting angle of the focusing lens. When the tilting angle of the focusing lens is selected so that the focusing points coincide with focusing points in the respective planes in the cavity mode, astigmatism-compensated pumping light is obtained. The invention is achieved by paying attention to the above.
In the laser cavity, a gain crystal and a dichroic concave mirror are provided. The dichroic concave mirror functions as a concave mirror in the cavity mode to obtain a focus on the inside of the gain crystal and functions as a concave lens for pumping light. The position and angle of the focusing lens are designed so that the pumping light passes through the focusing lens and the concave lens and comes into a focus in the gain crystal so as to almost coincide with the focusing point in the cavity mode. When the focusing point in the sagittal plane and that in the tangential plane do not coincide with each other, however, astigmatism occurs and a laser does not operate as a stable Kerr-lens mode-locked laser. According to the invention, therefore, the focusing lens is tilted with respect to the optical axis of pumping light, and a synthetic focusing point of the focusing lens, the concave lens, and the gain crystal in a sagittal plane and that in a tangential plane are independently calculated as functions of the tilting angle of the focusing lens. The tilting angle of the focusing lens is determined so that the focusing points almost coincide with focusing points in the respective planes in the gain crystal in the cavity mode.